Luminosity monitoring and search for an $e^{/emph>\mathrm{}}$ through eγ scattering at $e^{+}$$e^{\mathrm{-}}$ colliders

At $e^{+}$ $e^{\mathrm{-}}$ supercolliders such as the Stanford Linear Collider or CERN LEP, we suggest the use of eγ scattering (where the photons are quasireal ones, generated by one of the $e^{\pm }$ beams and interacting with the other) for the monitoring of experimental luminosities. The same process may also be used for searching for an $e^{\mathrm{*}}$, or determining a limit for its coupling constant, practically in the full mass range covered by such colliders. We discuss the experimental requirements and the results to be anticipated in that type of study.